Speaker: Prof. David Loeffler (UniDistance Swisse)

Title: Euler systems and Selmer group bounds at non-ordinary primes

Time: 14:00-15:00  April 17, 2026 (Friday)

Place: MCM110

Abstract: A key theme in Iwasawa theory is to study the sizes of Selmer groups attached to global Galois representations over the p-cyclotomic tower; this plays a key role in studying major open problems such as the Birch–Swinnerton-Dyer conjecture for elliptic curves. The theory of Euler systems has played a major role in this theory, serving to give upper bounds for Selmer groups.

However, when the Galois representation does not satisfy some kind of "ordinarity" condition at p, even defining these Selmer groups becomes substantially more difficult. About 10 years ago, Pottharst introduced a beautiful new formalism for defining Selmer groups using ideas from p-adic Hodge theory, which works uniformly for ordinary and non-ordinary primes; but so far it has seemed difficult to use Euler systems to study Pottharst's Selmer groups. I will report on a new breakthrough using the notion of "ultraprimes" introduced by Scholze and Sweeting, which has made it possible to relate Euler systems to Pottharst's theory, and explain applications to the Iwasawa main conjecture for Rankin-Selberg convolutions and for GSp(4) at non-ordinary primes.